Instead of maximizing \(p_{\mathbf {\theta }}(y|\mathbf {x})\)  as in standard softmax classifier, following JEM [1]} we maximize the joint distribution \(p_{\mathbf {\theta }}(\mathbf {x},y)\) , which follows a mixture of Gaussians distribution in GMMC. To optimize \(\log p_{\mathbf {\theta }}(\mathbf {x},y)\) , we can consider three different approaches.
<FIGURE>